Bulk and isospin instabilities in hot nuclear matter

The instability of hot asymmetric nuclear matter with respect to bulk density distortions is considered. The equation of state of the extended Thomas-Fermi approximation is used. The origin of the anomalous dispersion and the influence of the Fermi-surface distortion effects on the bulk and isospin instabilities in homogenous nuclear matter are investigated. It is shown that the development of both instabilities is reduced significantly due to the Fermi-surface distortion effects. The dependence of the bulk instability on the temperature and on the multipolarity of the particle density distortions are shown for the nucleus of ${}^{208}\mathrm{Pb}$. The dependence of the formation of the decay modes (fission or multifragmentation) of the nuclei on the temperature and the Fermi-surface distortion effects are demonstrated. It is shown that in the case of low temperatures the preferable mode for the bulk instability is binary fission. For higher temperatures, the preferred modes are the multifragmentations for small clusters. The number of clusters increases with increasing temperature.

Figure 1

The density dependence of the incompressibility coefficient $K\left({\rho }_0\right)$ for different temperatures $T=0,8$, and 14 MeV (shown) for Skyrme interactions $\mathrm{Sk}{\mathrm{M}}^{*}$ (dotted lines), KDE0v1 (solid lines), and SLy230b (dashed lines).

Figure 2

The same as in Fig. 1 but for symmetry energy coefficient $C_{\mathrm{sym}}.$

Figure 3

The dependence of the isoscalar instability growth rate ${\mathrm{\Gamma }}_{+}\left(q\right)$ on the wave-number $q$ (in units of $k_F=p_F/\hslash )$. The solid curves are for the Fermi liquid for different temperatures (shown near the solid curves in MeV) with bulk density ${\rho }_0=0.3{\rho }_{\mathrm{eq}}\left(T\right)$ and the relaxation parameter $\beta =9.2$ MeV [see Eq. (15)]. The dashed line is the result for the nonviscous liquid without the Fermi-surface distortion effects at temperature $T=2\mathrm{MeV}$. The calculations were performed for the KDE0v1 interaction.

Figure 4

The dependence of the isovector instability growth rate ${\mathrm{\Gamma }}_{-}\left(q\right)$ on the wave-number $q$ (in units of $k_f=p_F/\hslash )$. The solid curves are for the Fermi liquid for different temperatures (shown near the solid curves in MeV) with bulk density ${\rho }_0=6{\rho }_{\mathrm{eq}}\left(T\right)$ and the relaxation parameter $\beta =4.6$ MeV [see Eq. (15)]. The dashed line is the result for the nonviscous liquid without the Fermi-surface distortion effects at temperature $T=2\mathrm{MeV}$. The calculations were performed for the $\mathrm{Sk}{\mathrm{M}}^{*}$ interaction.

Figure 5

The dependence of the isoscalar instability growth rate ${\mathrm{\Gamma }}_{+}\left(L\right)$ on the multipolarity $L$ of the particle density fluctuations for the nucleus of ${}^{208}\mathrm{Pb}$ for different temperatures. $T=0.5$, 4, 6, and $8\mathrm{MeV},$ which are shown near the curves. The calculations were performed for the KDE0v1 interaction.